Two-dimensional global manifolds of vector fields

We describe an efficient algorithm for computing two-dimensional stable and unstable manifolds of three-dimensional vector fields. Larger and larger pieces of a manifold are grown until a sufficiently long piece is obtained. This allows one to study manifolds geometrically and obtain important features of dynamical behavior. For illustration, we compute the stable manifold of the origin spiralling into the Lorenz attractor, and an unstable manifold in zeta(3)-model converging to an attracting limit cycle

Lasing at the band edges of plasmonic lattices

We report room temperature lasing in two-dimensional diffractive lattices of silver and gold plasmon particle arrays embedded in a dye-doped polymer that acts both as waveguide and gain medium. As compared to conventional dielectric distributed feedback lasers, a central question is how the underlying band structure from which lasing emerges is modified by both the much stronger scattering and the disadvantageous loss of metal. We use spectrally resolved back-focal plane imaging to measure the wavelength- and angle dependence of emission below and above threshold, thereby mapping the band structure. We find that for silver particles, the band structure is strongly modified compared to dielectric reference DFB lasers, since the strong scattering gives large stop gaps. In contrast, gold particles scatter weakly and absorb strongly, so that thresholds are higher, but the band structure is not strongly modified. The experimental findings are supported by finite element and fourier modal method calculations of the single particle scattering strength and lattice extinction.Comment: 10 pages, 8 figure

Genetic Markers as Instrumental Variables

The use of genetic markers as instrumental variables (IV) is receiving increasing attention from epidemiologists, economists, statisticians and social scientists. This paper examines the conditions that need to be met for genetic variants to be used as instruments. Although these have been discussed in the epidemiological, medical and statistical literature, they have not been well-defined in the economics and social science literature. The increasing availability of biomedical data however, makes understanding of these conditions crucial to the successful use of genotypes as instruments for modifiable risk factors. We combine the econometric IV literature with that from genetic epidemiology using a potential outcomes framework and review the IV conditions in the context of a social science application, examining the effect of child fat mass on academic performance.ALSPAC; Fat mass; Genetic Variants; Instrumental Variables; Mendelian Randomization; Potential Outcomes

Genetic Markers as Instrumental Variables:An Application to Child Fat Mass and Academic Achievement

The use of genetic markers as instrumental variables (IV) is receiving increasing attention from economists. This paper examines the conditions that need to be met for genetic variants to be used as instruments. We combine the IV literature with that from genetic epidemiology, with an application to child adiposity (fat mass, determined by a dual-energy X-ray absorptiometry (DXA) scan) and academic performance. OLS results indicate that leaner children perform slightly better in school tests compared to their more adipose counterparts, but the IV findings show no evidence that fat mass affects academic outcomes.Instrumental variables; Mendelian randomization; Genetic variant; Potential outcomes; Academic performance; Educational attainment; Adiposity; Fat mass; Body Mass Index; ALSPAC

Child height, health and human capital: evidence using genetic markers

Height has long been recognised as associated with better outcomes: the question is whether this association is causal. We use children’s genetic variants as instrumental variables (IV) to deal with possible unobserved confounders and examine the effect of child and adolescent height on a wide range of outcomes: academic performance, IQ, self-esteem, symptoms related to depression and behavioural problems, including hyperactivity, emotional, conduct and peer problems. OLS findings show that taller children have higher IQ scores, perform better in school tests, and are less likely to have emotional or peer problems. The IV results differ. They show that taller children have better cognitive performance but, in contrast to the OLS, indicate that taller children are more likely to have behavioural problems. The magnitude of these IV estimates is large. For example, the effect of one standard deviation increase in height on IQ is comparable to the IQ difference for children born approximately 6 months apart within the same school year, while the increase in hyperactivity is comparable to the raw difference in hyperactivity between boys and girls.Child and adolescent height; human capital; mental health; behavioural outcomes; instrumental variables; Mendelian randomization; genetic variants; ALSPAC

Genetic markers as instrumental variables: an application to child fat mass and academic achievement

The use of genetic markers as instrumental variables (IV) is receiving increasing attention from economists. This paper examines the conditions that need to be met for genetic variants to be used as instruments. We combine the IV literature with that from genetic epidemiology, with an application to child adiposity (fat mass, determined by a dual-energy X-ray absorptiometry (DXA) scan) and academic performance. OLS results indicate that leaner children perform slightly better in school tests compared to their more adipose counterparts, but the IV findings show no evidence that fat mass affects academic outcomes.

Genetic markers as instrumental variables

AbstractThe use of genetic markers as instrumental variables (IV) is receiving increasing attention from economists, statisticians, epidemiologists and social scientists. Although IV is commonly used in economics, the appropriate conditions for the use of genetic variants as instruments have not been well defined. The increasing availability of biomedical data, however, makes understanding of these conditions crucial to the successful use of genotypes as instruments. We combine the econometric IV literature with that from genetic epidemiology, and discuss the biological conditions and IV assumptions within the statistical potential outcomes framework. We review this in the context of two illustrative applications